A multi-speed type automatic transmission is well known that includes a plurality of engagement devices and that is shifted to each of a plurality of gear shift positions by switching an engagement state of the plurality of engagement devices. This corresponds to an automatic transmission described in Patent Document 1. Patent Document 1 discloses that when it is predicted that a power-on downshift is required as a next shift, a hydraulic pressure is supplied to an engagement-side engagement device to be engaged in the next shift for achieving a standby state immediately before starting the engagement in advance, specifically, a state in which a space is eliminated between a piston and an engagement element constituting the engagement-side engagement device and the engagement element does not yet have a torque capacity. By supplying the hydraulic pressure in advance to the engagement-side engagement device, a delay of the start of the next shift is prevented, and a drive force can be improved in responsiveness to a driver's operation.